Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.
What is the ruling on giving the expiation of an oath (Kaffarat al-Yamin) to a charity that feeds the poor?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is allowed for a Muslim to appoint a proxy (agent) to distribute the expiation (Kaffarah) on their behalf. Our jurists have explicitly stated the permissibility of delegation (Tawkil) in the distribution of Zakat, Kaffarah, and vows (Nadr).
It is stated in Mughni al-Muhtaj (Vol.3/P.237): 'One has the right to pay the Zakat of their wealth personally... and they also have the right to delegate it.' And Allah the Exalted knows best.
Is supplicating in Qunoot, at times of affliction, during obligatory and voluntary prayer a Sunnah, and should it be done before Rukoo` (bowing), or after it?
At times of affliction, it is a Sunnah that Muslims supplicate in Qunoot after the final Rukoo` of each obligatory, or voluntary prayer as individuals, or in congregation.
What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.